are you asking about serial dilution of the cells or serial dilution of the selection agent (antibiotic)?

If you are talking about the selection agent, you do a serial dilution when you do not know the correct concentration of agent to effectively kill off the untransfected cells while keeping your positive cells alive. You only need to do this once in order to determine the concentration to use in subsequent transfections.

The protocol you have is for generation of monoclonal stably transfected cells. You need to dilute the cells out to obtain colonies starting from single cells, without the cells all dying (they like to have other cells around). It also helps so that you can determine the effective density for antibiotic selection, most antibiotics will have an optimal selection density that is less than 30% confluent. You can determine the optimal density and concentration of antibiotic before starting transfections by doing serial dilutions of both cells and antibiotics